A symmetry preserving contact interaction treatment of the kaon

TL;DR

This paper introduces a symmetry-preserving regularization method for contact interaction models, enabling consistent calculations of kaon properties while maintaining gauge invariance and addressing divergence issues.

Contribution

A novel regularization procedure that preserves gauge symmetry and Ward-Takahashi identities in contact interaction models is proposed and applied to kaon form factors.

Findings

Successfully computed kaon electromagnetic form factor

Obtained self-consistent $K_{l3}$ transition form factor results

Regularization handles divergences without inconsistencies

Abstract

A symmetry-preserving regularization procedure for dealing with the contact interaction model is proposed in this work. This regularization procedure follows a series of consistency conditions which are necessary to maintain gauge symmetry. Under this regularization, proofs for the preservation of the Ward-Takahashi identities are given and the loop integrals in the contact interaction model are systematically computed. As an application example, the kaon electromagnetic form factor and $K_{l3}$ transition form factor are computed and self-consistent results are obtained. Since the proposed regularization properly handles the divergence, one is freed from the inconsistencies caused by the regularization and can concentrate more on the physical discussion.